Pressure-induced spin collapse of octahedrally coordinatedFe3+inCa3Fe2[SiO4]3from experiment and theory

Abstract

The high-pressure behavior of andradite garnet, ${\mathrm{Ca}}_{3}{\mathrm{Fe}}_{2}{\mathrm{[SiO}}_{4}$]${}_{3}$, was studied at pressures up to 80 GPa using single-crystal synchrotron x-ray diffraction, Raman spectroscopy, and quantum mechanical calculations based on density functional theory. An isosymmetric phase transition was observed in the pressure range between 60 and 70 GPa, which is associated with a gradual high-spin to low-spin electronic transition in ${\mathrm{Fe}}^{3+}$. Experimental structural data before and after the phase transition are in excellent agreement with the theoretically predicted structural compression of the high-spin and low-spin phases, respectively. While the overall unit-cell volume is reduced by about $2.5%$ across the phase transition, a collapse of about $10%$ of the ${\mathrm{FeO}}_{6}$ octahedral volume is observed, attributed to the reduced Fe--O bond lengths associated with low-spin ${\mathrm{Fe}}^{3+}$. In combination with earlier data the present study shows that a spin collapse of ${\mathrm{Fe}}^{3+}$ in ${\mathrm{FeO}}_{6}$ octahedra will be triggered if the Fe--O bond length reaches a critical value of $d$(Fe--O) $<$ $\ensuremath{\approx}$ 1.9 \AA{}. Earlier reported results for the compressibility of the cation coordination polyhedra are substantially revised, with ${B}_{{\mathrm{FeO}}_{6}}=195(2)$ GPa, ${B}_{{\mathrm{CaO}}_{8}}=104(2)$ GPa, and ${B}_{{\mathrm{SiO}}_{4}}=348(11)$ GPa for the high-spin phase. The mode Gr\"uneisen parameters range between 0.61 and 1.34. The computed spin-pairing energy is $\ensuremath{\approx}4.2$ eV at 0 GPa.